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Kriging of financial term-structures

Areski Cousin (), Hassan Maatouk () and Didier Rulliere ()
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Areski Cousin: SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1
Hassan Maatouk: Ecole Nationale Supérieure des Mines de St Etienne, GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques - CNRS - Centre National de la Recherche Scientifique

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Abstract: Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension.

Keywords: interest-rate curve; kriging; implied default distribution; OIS discount curve; Model risk; yield curve; no-arbitrage constraints (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2016-06-04
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01206388v2
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Published in European Journal of Operational Research, Elsevier, 2016, 255 (2), pp.631-648.

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Journal Article: Kriging of financial term-structures (2016) Downloads
Working Paper: Kriging of financial term-structures (2016) Downloads
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